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          <th colspan="3" align="center">Appendix E. Modal Frequency Ratios</th>
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            <h1 class="title"><a id="MiscModalFreq"></a>Appendix E. Modal Frequency Ratios</h1>
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      <h2><a id="idp235284672"></a>Contributed by Scott Lindroth</h2>
      <p>
    John Bower, a student of Scott Lindroth, compiled this list of modal frequencies for various objects and materials. Some modes work better than others, and most need to be in a particular frequency range to sound plausible. Caveat emptor.
  </p>
      <p>
    In general, wooden objects will not sound "wooden" unless a stochastic component is present in the sound (try banded waveguides). Nonetheless, some of the wooden objects make wonderful metallic instruments as well.
  </p>
      <p>
    This ratios can be useful together with opcodes like <a class="link" href="mode.html" title="mode"><em class="citetitle">mode</em></a> or <a class="link" href="streson.html" title="streson"><em class="citetitle">streson</em></a>.
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          <strong>Table E.1. Modal Frequency Ratios</strong>
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          <table summary="Modal Frequency Ratios" border="1">
            <colgroup>
              <col />
              <col />
            </colgroup>
            <thead>
              <tr>
                <th>Instrument</th>
                <th>Modal Frequency Ratios</th>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td>Dahina tabla</td>
                <td>[1, 2.89, 4.95, 6.99, 8.01, 9.02]</td>
              </tr>
              <tr>
                <td>Bayan tabla</td>
                <td>[1, 2.0, 3.01, 4.01, 4.69, 5.63]</td>
              </tr>
              <tr>
                <td>Red Cedar wood plate</td>
                <td>[1, 1.47, 2.09, 2.56]</td>
              </tr>
              <tr>
                <td>Redwood wood plate</td>
                <td>[1, 1.47, 2.11, 2.57]</td>
              </tr>
              <tr>
                <td>Douglas Fir wood plate</td>
                <td>[1, 1.42, 2.11, 2.47]</td>
              </tr>
              <tr>
                <td>uniform wooden bar</td>
                <td>[1, 2.572, 4.644, 6.984, 9.723, 12]</td>
              </tr>
              <tr>
                <td>uniform aluminum bar</td>
                <td>[1, 2.756, 5.423, 8.988, 13.448, 18.680]</td>
              </tr>
              <tr>
                <td>Xylophone</td>
                <td>[1, 3.932, 9.538, 16.688, 24.566, 31.147]</td>
              </tr>
              <tr>
                <td>Vibraphone 1</td>
                <td>[1, 3.984, 10.668, 17.979, 23.679, 33.642]</td>
              </tr>
              <tr>
                <td>Vibraphone 2</td>
                <td>[1, 3.997, 9.469, 15.566, 20.863, 29.440]</td>
              </tr>
              <tr>
                <td>Chalandi plates</td>
                <td><p>([62, 107, 360, 460, 863] Hz +-2Hz)</p>
            <p>[1, 1.72581, 5.80645, 7.41935, 13.91935] ratios</p></td>
              </tr>
              <tr>
                <td>tibetan bowl (180mm)</td>
                <td><p>( [221, 614, 1145, 1804, 2577, 3456, 4419] Hz) 934g, 180mm</p>
            <p>[1, 2.77828, 5.18099, 8.16289, 11.66063, 15.63801, 19.99 ratios</p></td>
              </tr>
              <tr>
                <td>tibetan bowl (152 mm)</td>
                <td><p>([314, 836, 1519, 2360, 3341, 4462, 5696] Hz) 563g, 152mm</p>
            <p>[1, 2.66242, 4.83757, 7.51592, 10.64012, 14.21019, 18.14027] ratios</p></td>
              </tr>
              <tr>
                <td>tibetan bowl (140 mm)</td>
                <td><p>([528, 1460, 2704, 4122, 5694] Hz) 557g, 140mm</p>
            <p>[1, 2.76515, 5.12121, 7.80681, 10.78409] ratios</p></td>
              </tr>
              <tr>
                <td>Wine Glass</td>
                <td>[1, 2.32, 4.25, 6.63, 9.38]</td>
              </tr>
              <tr>
                <td>small handbell</td>
                <td><p>([1312.0, 1314.5, 2353.3, 2362.9, 3306.5, 3309.4, 3923.8, 3928.2, 4966.6, 4993.7, 5994.4, 6003.0, 6598.9, 6619.7, 7971.7, 7753.2, 8413.1, 8453.3, 9292.4, 9305.2, 9602.3, 9912.4] Hz)</p>
            <p>[ 1, 1.0019054878049, 1.7936737804878, 1.8009908536585, 2.5201981707317, 2.5224085365854, 2.9907012195122, 2.9940548780488, 3.7855182926829, 3.8061737804878, 4.5689024390244, 4.5754573170732, 5.0296493902439, 5.0455030487805, 6.0759908536585, 5.9094512195122, 6.4124237804878, 6.4430640243902, 7.0826219512195, 7.0923780487805, 7.3188262195122, 7.5551829268293 ] ratios</p></td>
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              <tr>
                <td>spinel sphere with diameter of 3.6675mm</td>
                <td><p>([977.25, 1003.16, 1390.13, 1414.93, 1432.84, 1465.34, 1748.48, 1834.20, 1919.90, 1933.64, 1987.20, 2096.48, 2107.10, 2202.08, 2238.40, 2280.10, 0 /*2290.53 calculated*/, 2400.88, 2435.85, 2507.80, 2546.30, 2608.55, 2652.35, 2691.70, 2708.00] Hz)</p>
            <p>[ 1, 1.026513174725, 1.4224916858532, 1.4478690202098, 1.4661959580455, 1.499452545408, 1.7891839345101, 1.8768994627782, 1.9645945254541, 1.9786543873113, 2.0334612432847, 2.1452852391916, 2.1561524686621, 2.2533435661294, 2.2905090816065, 2.3331798413917, 0, 2.4567715528268, 2.4925556408289, 2.5661806088514, 2.6055768738808, 2.6692760296751, 2.7140956766436, 2.7543617293425, 2.7710411870043 ] ratios</p></td>
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              <tr>
                <td>pot lid</td>
                <td>
                  <p>[ 1, 3.2, 6.23, 6.27, 9.92, 14.15] ratios</p>
                </td>
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